In the case of \({\cal N}\) -extended Poincaré supersymmetry, higher-spin generalisations of the linearised super-Cotton tensor were given in
[1]}, [2]} for \({\cal N}=1\) , in [3]} for \(\mathcal {N}=2\)  and in [4]} for \({\cal N}>2\) .
Below we generalise the results of [1]}, [2]} to the \({\cal N}=1\)  AdS supersymmetry,
while the \({\cal N}>1\)  case will be discussed elsewhere.
